Pricing Of Guaranteed Lifetime Withdrawal Benefit In Variable Annuities And Analysis Of Longevity Risk

Recalling the development process of the Guaranteed Minimum Withdrawal Benefits in variable annuities, the latest innovation is the promotion of a lifetime GMWB(GMWB for life; lifetime GMWB; GLWB). Unlike GMWB, GLWB provides policyholders a lifelong income; there is no limit in the total amount which the policyholders can be withdrawal. As long as the policyholder survives, he can continue to withdrawal guaranteed amount from his annuity until his death, no matter how the contract account value performs. GLWB was first introduced in the US market in 2003. Due to the long-term contract period, it has become one of the important pension plans of retired, and one of the most popular annuity products in the pension market. Being a type of a life annuity with benefit linked to the equity market, insurers who offer GLWB embedded in variable annuities are subject to several types of risk, esp ecially the longevity risk, which is caused by the further extension of the life expectancy. We must carry out an analysis of the impact of longevity risk on the GLWB value, since it is cannot be eliminated by the law of large numbers.This thesis first describes the general definition and features of GLWB, while analyzing the impact of several types of risk on the GLWB. Tractab le continuous-time models are specified to capture mortality risk underlying GLWB in variable annuities. We evaluate GLWB using two approaches, from the perspective of the policyholder and the insurer, which is shown to be equivalent. Using the model from the perspective of the policyholder, we study the fair guarantee fee rates of GLWB which is subject to various provisions. Then, we analyze the impact of longevity risk on the GLWB pricing, as well as other types of risk; and we compare the fair guaranteed fee under fixed and stochastic mortality risk model, by solving the P&L distribution of the insurer. Finally, we make recommendations on pricing and risk management for GLWB annuities. The thesis analyzes the impact of the longevity risk from the perspective of quantitative and qualitative, it has a strong application background and research value on the risk management of variable annuities and the promotion of the GLWB products.